Area of a Hemisphere Calculator
Enter a radius and get the surface area of a hemisphere — the total 3πr², the curved dome on its own, the flat circular base, and the volume too.
Total surface area (A = 3π·r²)
339.292007 square units
- Curved surface — dome only (2π·r²)
- 226.194671
- Flat base — circle (π·r²)
- 113.097336
- Volume (V = 2⁄3·π·r³)
- 452.389342
- Diameter (d = 2r)
- 12
A hemisphere is half a sphere. Its total surface area is the curved dome (2π·r², exactly half the sphere’s 4π·r²) plus the flat circular base (π·r²), giving 3π·r². For an open dome with no base, use the curved figure alone. The volume is half the sphere’s: (2⁄3)·π·r³.
How to use this calculator
Type the radius (r) of your hemisphere — the distance from the centre of the flat face out to the curved surface — in any unit you like: centimetres, metres, inches, feet. The calculator returns the total surface area (3πr²) as the headline figure, then breaks it into the curved dome (2πr²) and the flat circular base (πr²), and also gives the volume ((2⁄3)πr³) and the diameter. Because every output scales with a fixed power of the radius, the unit you type in is simply carried through: lengths stay in your unit, areas come out in that unit squared, and volume in that unit cubed.
How the calculation works
A hemisphere is a sphere sliced exactly in half through its centre, so its formulas come straight from the sphere’s. A full sphere has surface area 4πr²; half of that curved surface is the dome, 2πr². Cutting the sphere exposes a flat circular face — a disc of area πr². Adding the two gives the total surface area of a solid hemisphere: 2πr² + πr² = 3πr². If your dome is open or hollow (no flat lid), use the curved figure 2πr² on its own. The volume is likewise half the sphere’s: (1⁄2)·(4⁄3)πr³ = (2⁄3)πr³. π is used at full machine precision and rounding happens only when the answer is displayed.
Worked example
Take a hemisphere of radius 6 units. The curved dome is 2π·6² = 72π ≈ 226.19 square units. The flat base is π·6² = 36π ≈ 113.10 square units. The total surface area is their sum, 108π ≈ 339.29 square units — the same as 3π·6². Its volume is (2⁄3)π·6³ = 144π ≈ 452.39 cubic units. As a check, a full sphere of radius 6 would have surface area 4π·6² = 144π and volume (4⁄3)π·6³ = 288π, and the hemisphere’s curved area and volume are each exactly half of those.
Frequently asked questions
What is the surface area of a hemisphere?
For a solid hemisphere it is 3πr², where r is the radius. That total is the curved dome (2πr², half a sphere’s 4πr²) plus the flat circular base (πr²). If the dome is open with no base — like a bowl’s outer skin — use 2πr² instead.
Why is the total area 3πr² and not 2πr²?
Halving a sphere gives the curved dome, 2πr². But the cut also creates a new flat face — a circle of area πr² — that the sphere never had. A closed, solid hemisphere includes that base, so its total surface area is 2πr² + πr² = 3πr². The 2πr² figure counts only the curved part.
What is the difference between the curved and total surface area?
The curved (or lateral) surface area, 2πr², is just the rounded dome. The total surface area, 3πr², adds the flat circular base. Use the curved figure for hollow or open domes (a glass dome, half a hollow ball); use the total for a solid object whose flat face is a real surface.
How do I find the volume of a hemisphere?
The volume is (2⁄3)πr³ — exactly half a sphere’s (4⁄3)πr³. For radius 6 that is 144π ≈ 452.39 cubic units. This calculator shows the volume alongside the surface areas so you can size and cost a dome in one step.
Do the units matter?
Only that you are consistent. Enter the radius in whatever unit you like; the surface areas come back in that unit squared and the volume in that unit cubed. There is no hidden assumption of metres or inches — the geometry is unit-free, so feet in means square feet out.
Is a hemisphere the same as a semicircle?
No. A semicircle is a flat, two-dimensional half-disc, and its "area" (½πr²) is a flat region. A hemisphere is a three-dimensional half-ball, and its area is the surface wrapping that solid (3πr² total). This calculator handles the 3-D hemisphere; for the flat half-disc you want a circle-area calculator.